1. Preheat oven to 350 degrees. Spray a 9-by-13-inch baking pan with vegetable cooking spray.
2. Heat 1 tablespoon dipping oil in a large nonstick skillet over medium-high heat. When hot add mushrooms and garlic. Cook until mushrooms give off their liquid and begin to brown. Then stir occasionally until all the liquid has been cooked off, 12 to 14 minutes.
3. While mushrooms cook, prepare the sauce. Heat olive oil in a large saucepanover medium heat. Sprinkle in flour and stir to combine. Cook, stirring frequently, until mixture begins to turn a very light tan, about 3 minutes. Slowly whisk in evaporated milk, salt, nutmeg, and pepper. Stirring frequently, bring to a simmer. Once mixture simmers, turn off heat; it should be thickened enough to coat the back of a spoon. Set aside 1 1/3 cups of sauce. Whisk squash and chicken broth into the remaining sauce.
4. In a medium bowl, stir together the spinach and 1/3 cup of the reserved white sauce. When the mushrooms finish cooking, transfer them to a bowl and stir in another 1/3 cup white sauce.
5. Add remaining 1 tablespoon dipping oil to the pan used for the mushrooms. Reduce heat to medium and add the onion. Cook and stir until softened and lightly browned, about 8 minutes.
6. Assemble the lasagna. Pour remaining 2/3 cup white sauce into the prepared baking pan and spread it over the bottom. Lay 4 lasagna sheets in the pan and top with the entire spinach mixture, then 1 cup of the Swiss cheese and 1 cup of the squash sauce.
7. Top with 4 more sheets, then all the sausage, all the onion, 1 cup squash sauce, and 1/3 cup of the Parmesan.
8. Top with 4 more sheets, all the mushrooms, remaining 1 cup Swiss, and 1 cupsquash sauce. Top with 4 remaining sheets. Spread remaining squash sauce over pasta and sprinkle remaining 1/3 cup Parmesan over the top. Spray a large sheet of foil with vegetable cooking spray and cover the pan, sprayed side down.
9. Bake, covered, for 30 minutes. Remove foil and bake until bubbly and beginning to brown, an additional 20 to 25 minutes.
10. Let lasagna rest for 10 to 15 minutes, then cut into squares and serve.
Source: Hannaford fresh Magazine, January - February 2012